Document Zbl 0222.46039

Hilbert space representations of Lie algebras. (English) Zbl 0222.46039

Commun. Math. Phys. 23, 159-168 (1971).

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MSC:

46L60	Applications of selfadjoint operator algebras to physics
46J99	Commutative Banach algebras and commutative topological algebras
46A55	Convex sets in topological linear spaces; Choquet theory
22E70	Applications of Lie groups to the sciences; explicit representations

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[1]	Dixmier, J.: LesC*-algèbres et leurs représentations, cahiers scientifiques, fasc xxix. Paris: Gauthiers-Villars 1964.
[2]	Godement, R.: A theory of spherical functions I. Trans. Amer. Math. Soc.73, 496–556 (1952). · Zbl 0049.20103 · doi:10.1090/S0002-9947-1952-0052444-2
[3]	Goodman, R.: Analytic domination by fractional powers of a positive operator. J. Functional Anal.3, 246–264 (1969). · Zbl 0172.40605 · doi:10.1016/0022-1236(69)90042-1
[4]	—- Analytic and entire vectors for representations of Lie groups. Trans. Amer. Math. Soc.143, 55–76 (1969). · Zbl 0189.14102 · doi:10.1090/S0002-9947-1969-0248285-6
[5]	Harish-Chandra: Representations of a semi-simple Lie group on a Banach space, I. Trans. Amer. Math. Soc.75, 185–243 (1953). · Zbl 0051.34002 · doi:10.1090/S0002-9947-1953-0056610-2
[6]	Nelson, E.: Analytic vectors. Ann. of Math.70, 572–615 (1959). · Zbl 0091.10704 · doi:10.2307/1970331
[7]	Phelps, R.R.: Lectures on Choquet’s theorem. Princeton, New Jersey: van Nostrand 1966. · Zbl 0135.36203
[8]	Powers, R.T.: Self-adjoint algebras of unbounded operators. Commun. math. Phys.21, 85–124 (1971). · Zbl 0214.14102 · doi:10.1007/BF01646746
[9]	Segal, I.E.: Hypermaximality of certain operators on Lie groups. Proc. Amer. Math. Soc.3, 13–15 (1952). · Zbl 0049.35704 · doi:10.1090/S0002-9939-1952-0051240-5

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